This comprehensive work integrates knowledge from physics, chemistry, biology, mathematics, geology, engineering, and several other fields. Its purpose is to provide solution methods, techniques of parameter estimation, and tools for solving the complex problems of mathematical modeling. The main topics presented include fundamentals of mathematical modeling of migration processes; analytical, numerical, and inverse solutions to migration problems; and techniques of parameter estimation and monitoring of migration processes. The book is perfect for anyone involved in the areas of hydrogeology, soil science, environmental engineering, subsurface cleanup, water sciences, agronomy, land development, and civil engineering. It provides professionals with a survey of the methodology of migration model building, the mathematical tools for solving these models, and the technique of parameter estimation in laboratories and in the field. Consultants will appreciate the book's multidisciplinary theoretical background and first approximations for a broad variety of migration data. Professors and students gain an integrated survey of subsurface solute and heat transport, storage, transformation, and exchange processes in both theoretical and practical applications, complete with example problems and solutions.
METHODS OF MATHEMATICAL MODELLING. MODEL CONCEPTS FOR AIR, WATER, AND SOLIDS. Characterization of Multi-Component Systems. Mixphase Model of Air. Mixphase Model of Water. Mixphase Model of the Rock Matrix. SUBSURFACE MODEL CONCEPT. Scale of Observation. The "Mobile/Immobile" Two-Phase Model Approach. Multi-Fluid Immiscible Flow Model Approach. Concepts for Limiting Cases of Fluid Distribution and Flow. MASS TRANSPORT IN THE SUBSURFACE. Molecular Diffusion. Convection and Hydrodynamic Dispersion. Scale Problems of Hydrodynamic Dispersion. Applicability of the Hydrodynamic Dispersion Model Approach. PHASE INTERNAL CONVERSION PROCESSES. Fundamentals of Chemical Thermodynamics. Association and Dissociation of Particles in Solution. Acid-Base Reaction Processes. Oxidation-Reduction Processes. PHASE EXCHANGE. Dynamics of Exchange Processes. Exchange Processes. Dissolution and Precipitation Processes. Biological Metabolism of Migrants. Ecological Fundamentals. The Subsurface as a Living Space. Biogenic Substance and Energy Conversion. STORAGE PROCESS MODELS. HEAT MIGRATION. Heat Transport in the Subsurface. Phase Exchange, Storage, and Transformation Processes. MATHEMATICAL DESCRIPTION OF THE TOTAL MIGRATION PROCESS. Process Assessment. Methodological Examples. Heat Migration in the Vadose Subsurface. Migration of Oxygen in the Aerated Subsurface. Deionization of Water in the Subsurface. Initial and Boundary Conditions. REFERENCES. SOLUTION METHODS. ANALYTICAL SOLUTION METHODS. Review of Important Solution Methods. Solution of Convective Models. Solution of Diffusive/Dispersive Models. Solution of Dispersive-Convective Models. Computation of Analytical Solutions. NUMERICAL SOLUTION METHODS. Fundamentals of Building Discrete Migration Models. Formulation of Space-Discrete Mathematical Models. Formation of Time-Discrete Mathematical Models. Algorithms for One-and Quasi-One-Dimensional Migration Processes. Efficient Algorithms for Two-Dimensional Migration Processes. PARAMETER ESTIMATION. Fundamental Approach and Algorithm. Examples Using the "Straight-Line Method". Examples Using the "Type Curve Method". Example of Optimization with Objective Functions. REFERENCES. TECHNIQUES OF PARAMETER ESTIMATION. SAMPLING TECHNIQUE. Sampling Subsurface Solids. Collection of Soil-Water and Groundwater Samples. Soil-Air Sampling. TECHNIQUES FOR SAMPLE ANALYSIS. Analysis of Water and Air Samples. Migration Tests in Laboratories. Value of Parameters Determined from Samples. FIELD TEST METHODS. Geophysical Test Methods. Tests in the Natural Groundwater Flow. Pumping and Injection Tracer Tests. Seepage Tests. Value of Parameters Determined by Field Test Methods. MIGRATION PROCESS OBSERVATION AND INTERPRETATION. Monitoring Environmental Migrants. Monitoring of Migration Processes. REFERENCES.